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The book can be considered as an extended version of lecture notes which is prepared to cater the needs of each and every student in such a manner that they get ample material to understand each topic in different ways and by alternative approaches. The basic concepts and definitions in each unit have been discussed in detail in lucid manner with suitable illustrations. It is intended that the students will gain real understanding by firstly going through the solve problems and then solving the similar problems themselves. This book has been written for All Indian Technical Universities and strictly according to the latest syllabus prescribed by GBTU, Lucknow and MMTU, Noida. Plenty of solved examples have been given for each topic which help the students to tackle the maximum possible problems that can be formulated on any topic. A wide range of objective questions which touch each nook and corner of each unit have been added. By going through these questions, one can have a basic knowledge of each unit in context of its basic concepts and formulae used to initiated the advanced problems. The book also contains year wise (2000-2009) UPTU questions bank covering all the five units along with the previous years’s solved questions paper. Table of Contents Preface Acknowledgement UPTU Syllabus List of Important Formulae UNIT-1: Differential Calculus – I UNIT-2: Differential Calculus-II UNIT-3: Matrices UNIT-4: Multiple Integrals UNIT-5: Vector Calculus * UPTU Previous Years Questions (Sem. 1) Odd Semester Theory Examinations (2010-11).